定义：
计算与波长有关的折射率的方程。

表征透明光学材料中随波长变化的折射率时，通常采用Sellmeier公式[1]（也称为Sellmeier方程或Sellmeier色散公式）。典型的形式为： 

该形式是由一个简单的物理学模式推导出来的，该模型只适合于吸收可忽略的波长区域。 
例如，熔融二氧化硅的折射率可以计算为: 

其中波长单位是微米。 
可以采用最小二乘拟合过程得到Sellmeier系数，将其带入折射率表达式中可以计算很大波长范围内的折射率。 

应用 
由于该方程只需采用几个Sellmeier系数（根据一些测量数据进行最小二乘拟合得到）就可以在很大波长范围内准确给出折射率的值，所以用途非常广泛。许多材料的Sellmeier系数都在资料库中可以查到。当将Sellmeier方程用到某极限波长范围时，有一些需要注意的地方，但是目前还没有明确的规定波长适用范围。 
Sellmeier数据在计算材料色散时很重要。这牵涉到频率的倒数，即使存在高阶色散时，也可以采用Sellmeier数据进行分析，而将列表引用数据进行数值微分则对噪声非常敏感。 
Sellmeier另一个常用的地方是计算非线性频率转换过程中的相位匹配结构。需要保证Sellmeier数据在很宽的波长范围内是准确的。 

改进的方程 
方程具有一些改进的形式，仍被称为Sellmeier公式。将以上的简单形式拓展，可以扩大适用的波长范围，或者引入折射率随温度的变化关系。这在计算非线性频率转换过程中的相位匹配结构时非常重要。 

Sellmeier方程的替代方程 
还有其他的方程得到折射率。例如，柯西公式比Sellmeier方程更加简单，在可见光谱区域与许多材料的折射率都匹配的很好。但在近红外，Sellmeier方程可以得到更高的准确率。还有作者如， Hartmann, Conrady, Kettler–Drude, 和Herzberger等提出了其它的方程。

Definition: an equation for calculating the wavelength-dependent refractive index of a medium

For the specification of a wavelength-dependent refractive index of a transparent optical material (e.g. an optical glass), it is common to use a so-called Sellmeier formula [1] (also called Sellmeier equation or Sellmeier dispersion formula, after Wolfgang von Sellmeier). This is typically of the form

with the coefficients A_j and B_j. That form results from a relatively simple physical model with damped oscillators driven by the light field. Such a model is accurate only to the wavelength region where the absorption is negligible.

As an example, the refractive index of fused silica can be calculated as [2]

where the wavelength in micrometers has to be inserted.

The Sellmeier coefficients are usually obtained by a least-square fitting procedure, applied to refractive indices measured in a wide wavelength range.

Applications

Sellmeier equations are very useful, as they make it possible to describe fairly accurately the refractive index in a wide wavelength range with only a few so-called Sellmeier coefficients. Sellmeier coefficients for many optical materials are available in databases. Some caution is advisable when applying Sellmeier equations in extreme wavelength regions; unfortunately, the validity range of available data is often not indicated.

Sellmeier data can also be used for evaluating the chromatic dispersion of a material. This involves frequency derivatives, which can be performed analytically with Sellmeier data even for high orders of dispersion, whereas numerical differentiation on the basis of tabulated index data is sensitive to noise.

Another frequent application of Sellmeier data is the calculation of phase-matching configurations for nonlinear frequency conversion. Here, it is often critical to have Sellmeier data which are valid in a wide wavelength range.

Modified Equations

The literature contains a great variety of modified Sellmeier equations which are also often called Sellmeier formulas. Extensions to the simple form give above can enlarge the wavelength range of validity, or make it possible to include the temperature dependence of refractive indices. This can be important, for example, for calculating phase-matching configurations for nonlinear frequency conversion.

Alternatives to Sellmeier Equations

There are various other kinds of equations for refractive indices. For example, there is the old Cauchy formula, which is a bit simpler than the Sellmeier formula and still fits the refractive indices of many materials in the visible spectral region quite well, as long as the material has no absorption in the visible region. In the near infrared, however, substantially higher accuracy is achieved with the Sellmeier formula. Other equations have been presented by authors like Schott, Hartmann, Conrady, Kettler–Drude, and Herzberger. For example, the Schott formula is power series for calculating n².

Bibliography